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Unit - 1 Differential Calculus-1

Module1Differential calculus1

1.1 Review of elementary calculus curves angle between the radius vector and tangent

1.2 Angle between two curves pedal equation

1.3 Curvature and radius of curvatureCartesian and polar forms

1.4 Centre and circle of curvature All without proofformulae only applications to evolutes and involutes.

Unit - 2 Differential Calculus-2

Module2Differential calculus2

2.1. Taylors and Maclaurins series expansions for one variable statements only

2.2. Indeterminate forms LHospitals rule

2.3. Partial differentiation

2.4. Total derivativesdifferentiation of composite functions

2.5. Maxima and minima for a function of two variables

2.6. Method of Lagrange multipliers with one subsidiary condition

2.7. Applications of maxima and minima with illustrative examples

2.8. Jacobians simple problems

Unit - 3 Integral Calculus

Module3Integral Calculus

3.1. Review of elementary integral calculus multiple integrals Evaluation of double and triple integrals

3.2. Evaluation of double integrals change of order of integration and changing into polar co ordinates

3.3. Applications to find area volume and centre of gravity

3.4. Beta and Gamma functions Definitions Relation between beta and gamma functions and simple problems

Unit - 4 Ordinary differential equations of first order

Module4Ordinary differential equations of first order

4.1. Exact and reducible to exact differential equations

4.2. Bernoullis equation

4.3. Applications of ODEsorthogonal trajectories

4.4. Newtons law of cooling and L R circuits

4.5. Nonlinear differential equations Introduction to general and singular solutions

4.6. Solvable for p only

4.7. Clairauts and reducible to Clairauts equations only

Unit - 5 Linear Algebra

Module5Linear algebra

5.1. Rank of a matrixechelon form

5.2. Solution of system of linear equationsconsistency

5.3. Gausselimination method

5.4. GaussJordan method and approximate solution by GaussSeidel method

5.5. Eigen values and eigen vectors Rayleighs power method

5.6. Diagonalization of a square matrix of order two

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